Ali, Noor Aslinda and Abdul Aziz, Zainal (2013) Hirotasato formalism on some nonlinear waves equations. Jurnal Teknologi (Sciences and Engineering), 61 (1). pp. 16. ISSN 01279696

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Official URL: http://dx.doi.org/10.11113/jt.v61.1615
Abstract
This article demonstrates that Hirota’s direct method or scheme for solving nonlinear waves equation is linked to Sato theory, and eventually resulted in the Sato equation. This theoretical framework or simply the Hirota–Sato formalism also reveals that the τ – function, which underlies the analytic form of soliton solutions of theses physically significant nonlinear waves equations, shall acts as the key function to express the solutions of Sato equation. From representation theory of groups, it is shown that the τ – function in the bilinear forms of Hirota scheme are closely connected to the Plucker relations in Sato theory. Thus Hirota–Sato formalism provides a deeper understanding of soliton theory from a unified viewpoint. The Kadomtsev–Petviashvili (KP), Korteweg–de Vries (KdV) and Sawada–Kotera equations are used to verify this framework
Item Type:  Article 

Uncontrolled Keywords:  Hirota–Sato formalism, τ – function, Plucker relations; Kadomtsev–Petviashvili (KP) equation, Korteweg–de Vries (KdV) equation, Sawada–Kotera equation 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  50007 
Deposited By:  Siti Nor Hashidah Zakaria 
Deposited On:  02 Dec 2015 10:10 
Last Modified:  14 Oct 2018 16:26 
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